Results 11 to 20 of about 11,551,305 (305)
Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions [PDF]
Duke mathematical journal, 2020 We establish two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg, a theorem of Erdős-Delange, the mean value theorem of ...
V. Bergelson, F. Richter
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Explicit Kronecker–Weyl theorems and applications to prime number races [PDF]
Research in Number Theory, 2020 We prove explicit versions of the Kronecker–Weyl theorems, both in a discrete and a continuous settings, without any linear independence hypothesis. As an application, we propose an alternative approach to problems concerning asymptotic densities in ...
A. Bailleul
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A new elementary proof of the Prime Number Theorem [PDF]
Bulletin of the London Mathematical Society, 2020 Let Ω(n) denote the number of prime factors of n . We show that for any bounded f:N→C one has 1N∑n=1Nf(Ω(n)+1)=1N∑n=1Nf(Ω(n))+oN→∞(1).This yields a new elementary proof of the Prime Number Theorem.
F. Richter
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Blockchain Security Mechanism Design Based on Chinese Cryptosystem SM2 Algorithm
Mathematics, 2023 The cryptographic system is the foundation of blockchain security mechanisms. This paper constructs a blockchain security mechanism based on the Chinese national cryptographic SM2 algorithm, involving the generation of public–private key pairs and the ...
Lu Meng, Zeyao Liu
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Prime number theorem for analytic skew products [PDF]
Annals of Mathematics, 2020 We establish a prime number theorem for all uniquely ergodic, analytic skew products on the $2$-torus $\mathbb{T}^2$. More precisely, for every irrational $\alpha$ and every $1$-periodic real analytic $g:\mathbb{R}\to\mathbb{R}$ of zero mean, let $T_ ...
Adam Kanigowski +2 more
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Properties of Higher-Order Prime Number Sequences [PDF]
Missouri Journal of Mathematical Sciences, 2020 In this paper, we analyze properties of prime number sequences produced by the alternating sum of higher-order subsequences of the primes. We also introduce a new sieve which will generate these prime number sequences via the systematic selection and ...
Michael P. May
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Relation between Prime and Composite Number
Bibechana, 2018 This article was not peer-reviewed. No abstract available.
Raju Ram Thapa
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On the number of edges of a graph and its complement [PDF]
Arab Journal of Mathematical Sciences, 2021 Let G=(V,E) be a graph. The complement of G is the graph G¯:=(V,[V]2 \ E) where [V]2 is the set of pairs {x,y} of distinct elements of V. If K is a subset of V, the restriction of G to K is the graph G↾K:=(K,[K]2∩E).
Jamel Dammak +2 more
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The error term in the prime number theorem [PDF]
Mathematics of Computation, 2018 We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing
David J. Platt, Timothy S. Trudgian
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On the Universal Encoding Optimality of Primes
Mathematics, 2021 The factorial-additive optimality of primes, i.e., that the sum of prime factors is always minimum, implies that prime numbers are a solution to an integer linear programming (ILP) encoding optimization problem. The summative optimality of primes follows
Ioannis N. M. Papadakis
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